# Fair Dynamic Rationing

arXiv: https://arxiv.org/abs/2102.01240 · HTML: https://mlsanity.com/paper/2102.01240/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2021.

## Built on by (most cited first, 19 of 19)

- [Matching Algorithms for Blood Donation](https://mlsanity.com/paper/2108.04862/) (2021)
- [Fairness-aware Online Price Discrimination with Nonparametric Demand Models](https://mlsanity.com/paper/2111.08221/) (2021)
- [Fairness Maximization among Offline Agents in Online-Matching Markets](https://mlsanity.com/paper/2109.08934/) (2021)
- [Fairer LP-based Online Allocation via Analytic Center](https://mlsanity.com/paper/2110.14621/) (2021)
- [Fairness and Sequential Decision Making: Limits, Lessons, and Opportunities](https://mlsanity.com/paper/2301.05753/) (2023)
- [Utility Fairness in Contextual Dynamic Pricing with Demand Learning](https://mlsanity.com/paper/2311.16528/) (2023)
- [Fair Secretaries with Unfair Predictions](https://mlsanity.com/paper/2411.09854/) (2024)
- [Sequential Fair Resource Allocation under a Markov Decision Process Framework](https://mlsanity.com/paper/2301.03758/) (2023)
- [Time Fairness in Online Knapsack Problems](https://mlsanity.com/paper/2305.13293/) (2023)
- [Algorithmic Challenges in Ensuring Fairness at the Time of Decision](https://mlsanity.com/paper/2103.09287/) (2021)
- [Equity Promotion in Online Resource Allocation](https://mlsanity.com/paper/2112.04169/) (2021)
- [Stochastic Online Fisher Markets: Static Pricing Limits and Adaptive Enhancements](https://mlsanity.com/paper/2205.00825/) (2022)
- [Fair Incentives for Repeated Engagement](https://mlsanity.com/paper/2111.00002/) (2021)
- [Online Learning for Equilibrium Pricing in Markets under Incomplete Information](https://mlsanity.com/paper/2303.11522/) (2023)
- [Rethinking Algorithmic Fairness for Human-AI Collaboration](https://mlsanity.com/paper/2310.03647/) (2023)
- [Fair Allocation in Dynamic Mechanism Design](https://mlsanity.com/paper/2406.00147/) (2024)
- [Online Fair Allocation of Perishable Resources](https://mlsanity.com/paper/2406.02402/) (2024)
- [Modeling Access Differences to Reduce Disparity in Resource Allocation](https://mlsanity.com/paper/2402.00083/) (2024)
- [Fair Online Resource Allocation](https://mlsanity.com/paper/2606.18679/) (2026)

## Abstract (arXiv)

We study the allocative challenges that governmental and nonprofit organizations face when tasked with equitable and efficient rationing of a social good among agents whose needs (demands) realize sequentially and are possibly correlated. As one example, early in the COVID-19 pandemic, the Federal Emergency Management Agency faced overwhelming, temporally scattered, a priori uncertain, and correlated demands for medical supplies from different states. In such contexts, social planners aim to maximize the minimum fill rate across sequentially arriving agents, where each agent's fill rate is determined by an irrevocable, one-time allocation. For an arbitrarily correlated sequence of demands, we establish upper bounds on the expected minimum fill rate (ex-post fairness) and the minimum expected fill rate (ex-ante fairness) achievable by any policy. Our upper bounds are parameterized by the number of agents and the expected demand-to-supply ratio, yet we design a simple adaptive policy called projected proportional allocation (PPA) that simultaneously achieves matching lower bounds for both objectives (ex-post and ex-ante fairness), for any set of parameters. Our PPA policy is transparent and easy to implement, as it does not rely on distributional information beyond the first conditional moments. Despite its simplicity, we demonstrate that the PPA policy provides significant improvement over the canonical class of non-adaptive target-fill-rate policies. We complement our theoretical developments with a numerical study motivated by the rationing of COVID-19 medical supplies based on a standard SEIR modeling approach that is commonly used to forecast pandemic trajectories. In such a setting, our PPA policy significantly outperforms its theoretical guarantee as well as the optimal target-fill-rate policy.